5.1. Open and Closed Sets
Definition 5.1.1: Open and Closed Sets
A set U R is called open, if for each x U there exists an > 0 such that the interval ( x - , x + ) is contained in U. Such an interval is often called an -neighborhood of x, or simply a neighborhood of x.
A set F is called closed if the complement of F, R \ F, is open.